Chaotic interactions between dark matter and dark energy

In this study, we consider dark matter and dark energy as grand-canonical systems which are open, non-equilibrium coupled, and interacting systems. For the first time, we propose a new more realistic interaction scheme to explain dynamics between coupled interacting thermodynamic systems. Based on this new interaction schema, we propose new theorems to define the interactions including mutual and self-interactions. We proved the theorems based on the energy conservation law of thermodynamics. Furthermore, we obtain new coupled equations using the theorems. We numerically solved the interaction equations and obtained phase space diagrams and Lyapunov exponents. We show that the interaction between dark matter and dark energy is chaotic. We conclude that these theorems and results can be generalized to all coupled interacting particle and thermodynamic systems. Finally, we evaluated that the obtained results indicate the existence of a new law in physics. Additionally, based on the results, we gave physical definitions of basic concepts such as chaos and self-organization and pointed out the existence of hidden symmetries and variables in interacting systems.